Sleeping Dogs is awesome. It has a great story, plus there are lots of side missions and other stuff to do as well. If you're into first person-shooters I would recommend getting Battlefield 3 as well. If you're in the racing games however, you absolutely have to get Forza Motorsport 4. Best racing game ever.

Call of Duty and Gears of War 3 is still pretty active so lots of fun to be had there, actually playing GOW3 now after getting the season pass yesterday to get all the maps (cheaper that way still). Max Payne 3 also is not bad for a good shoot em up.

As has been said it really does depend hugely on what your tastes are.

Forza 4 is a great simulation racer that with all the challenges that renew every so often meaning you've always got something to do.
For ARPG's: Skyrim is the daddy but if you want a JPRG there's a lot of options, Final Fantasy XIII or for something slightly different, Lost Odyssey is amazing but also very long. You could also try Blue Dragon for something REALLY off the wall, bats**t crazy.
Shooters: Well you've got a lot of choice, depends on whether you like Call Of Duty or Battlefield, the latter is probably better to my tastes but you might prefer CoD.
Free Roam games, Crackdown (and 2) was always a good laugh, or you've got the new Sleeping Dogs, or Just Cause 2 (JC2 lasted me a HUGE amount of time and I still haven't really completed it)
Or you could go sport games: Tiger Woods (I prefer 12 over 13), Fifa if you like football (or soccer?), and 11 is probably my favourite. Or you could go American Football and choose Madden.
For platformers you're a little more limited, but you could do worse than choosing Prince Of Persia The Forgotten Sands, or the Prince Of Persia that came out before it. Both good games, eminently enjoyable but could be called short.

I am seriously not trying to start anything here, but can someone explain the hype of Halo to me? Over the years I have played most of the FPS's that the 360 had, but I never could understand the hype behind Halo. I never found it to even be that good to be honest. But then again, I still play World of Warcraft, as well as Starcraft, so that may have some sway in my decisions. I just don't understand the Halo hype, at all.